Stick Number Research Articles

STICK NUMBER OF THETA-CURVES

[5, 7]. Since this presentation of knots has been considered tobe a useful mathematical model of cyclic molecules or molecular chains,the stick number may be one of intrinsic properties which are interestednot only in knot theory of mathematics, but also in biology, chemistryand physics. In general it is not easy to determine s(

Kappa-Opioid Receptor Agonist Protects the Microcirculation of Skeletal Muscle From Ischemia Reperfusion Injury

Previous research has demonstrated that pretreatment with kappa opioid receptor (KOR) agonist protects against ischemia reperfusion (I/R) injury in cardiomyocytes and neuron cells through activation of protein kinase C. The purpose of this study is to investigate the KOR agonist's effect on I/R-injured cremaster muscle and its underlying mechanism. Male Sprague Dawley rats were randomized into 3 groups (n = 6 each group). Group I was the ischemia reperfusion (I/R) injury group (4 hours of ischemia followed by 90 minutes of reperfusion). Group II was the U-50488H (selective KOR agonist)-pretreated group (KOR agonist + I/R injury). Group III was pretreated with U-50488H + nor-binaltorphimine (NBI, a selective KOR antagonist) (KOR agonist + antagonist + I/R injury). The numbers of leukocyte rolling, adhering, and transmigrating, functional capillary, and swelling index of the vessel wall of the postcapillary venule were observed under intravital videomicroscopy. Biochemically, the lactate dehydrogenase, creatine phosphokinase isoenzyme, expression of E-selectin, and intercellular adhesion molecule-1 (ICAM-1) were analyzed. The U-50488H-pretreated group had significantly decreased the number of leukocyte sticking (P < 0.001) and transmigrating (P < 0.001) as compared with the I/R-injury group and the U-50488H + NBI-pretreated group. The numbers of functional capillary in the U-50488H-pretreated group were significantly less attenuated compared with the I/R-injury group and U-50488H + NBI-pretreated group (P < 0.001). The expression of the ICAM-1 in the cremaster muscle was evidently reduced in the U-50488H-pretreated group than in the I/R-injury group or the U-50488H + NBI-pretreated group. Administration of KOR agonist protects the muscle flap microcirculation from I/R injury, which can be abolished by concomitant KOR antagonist administration. The KOR agonist-induced protection from ischemia reperfusion injury may be related to decreased expression of adhesion molecule ICAM-1.

FIGURE-8 KNOT ON THE CUBIC LATTICE

We will examine the stick number of knots on the cubic lattice which is called the lattice stick number. The lattice stick numbers of knots <TEX>$3_1$</TEX> and <TEX>$4_1$</TEX> are known as 12 and 14, respectively. In this paper, we will show that only <TEX>$3_1$</TEX> and <TEX>$4_1$</TEX> have representations of irreducible non-trivial polygons, both numbers of whose sticks parallel to the y-axis and the z-axis are exactly four.

CLASP MOVES AND STICK NUMBER

We introduce a geometric construction, called a clasp move, which is used to prove several results on stick numbers of links. In particular, we show that all two-component six-crossing links have stick number 8, produce small crossing number knots that can be constructed with fewer sticks than crossings, and improve known upper bounds for the stick number of certain classes of links.

Performance of Gladiolus as Influenced by Boron and Zinc

The field study of B and Zn on Gladiolus was conducted at Floriculture Farm of HRC, Gazipur and RARS, Jessore during 2005-2006. The objective was to evaluate the response of B and Zn and to find out the optimum dose of the same for production of gladiolus. It appeared in studied data reveals that B and Zn made promising response to the growth and floral characters of gladiolus. It was also noticed in the tables that B and Zn both either in single or in combination exerted tremendous effect on the yield and quality of gladiolus. However, with subsequent addition of higher rates of B and Zn progressively increased the selective growth and flower characters to some extent and beyond the further increment of the dosage declined the results noticeably. It is also reported that gladiolus is highly responsive to chemical fertilizers. The sixteen treatment combinations included in the study noted that B and Zn at the rate of B2.0 Zn4.5 kg ha(-1). along with blanket dose of N375 P150 K250 S20 kg and CD 5 t ha(-1) exhibited the best performance in flower production and stretched the vase life of flower. The studied parameters like plant height (79.83 and 87.61 cm), length of spike (71.2 and 67.33 cm) length of rachis (48.86 and 45.08 cm) and leaves number (10.77 and 9.87/plant) significantly responded to the combined application of boron and zinc at the rate of B2.0 Zn4.54 as compared to other treatment combinations. Floral characters like floret number (12.85 and 12.45/spike), floret size (9.76x8.93 and 10.28x9.77 cm) and weight of stick (36.73 and 45.12 g) also significantly influenced by said treatment (B2.0 Zn4.5 kg ha(-1)) which was markedly differed over rest of treatments combination. Similar trend was noticed as well in single application of B and Zn with increase rates.

LATTICE STICK NUMBERS OF SMALL KNOTS

Lattice stick number sL(K) is defined to be the minimal number of sticks required to construct a polygonal representation of the knot K in the cubic lattice. In this paper, we give lattice stick numbers of small knots such as 31 and 41. More precisely we prove that sL(31) = 12 and sL(K) ≥ 14 for any other non-trivial knot K.

On stick number of knots and links

Abstract The DNA strand is made up of small rigid sticks of sugar, phosphorus, nucleotide proteins and hydrogen bond. A cyclic molecule can be modelled by a sequence of sticks glued end-to-end so that the last one is also glued to the first. Thus we have mathematical stick knots or polygonal knots. This gives rise to some questions: For instance, what is the smallest number of atoms needed to construct a nontrivial knotted molecule? For such stick numbers, Negami gave an upper and lower bound. In the case when a given knot reaches its lower bound in Negami’s inequality, we gave a specific relation between both of its stick and crossing numbers. Hence we conclude that not one of the knots, at least, to 26 crossings can achieve its lower bound. In other words every knotted molecule of atoms up to 26 will have a number of bonds more than the lower bound in Negami’s inequality. Subsequently it is shown that some interesting class of torus knots does not achieve that lower bound in Negami’s inequality.

Submucosal Collecting Venules: A Reliable Site for Intestinal Intravital Microscopy in Rats

Under physiological conditions and after interventions such as ischemia/reperfusion, postcapillary mesenteric venules are most commonly used for in vivo assessment of intestinal microcirculation by intravital microscopy (IVM). In experimental models of gut inflammation, however, IVM was found to be hampered by postinflammatory tissue injury. In this study, postcapillary submucosal collecting venules located at the junction of mesentery and ileum are introduced and evaluated for IVM in a rat model of indomethacin-induced ileitis. The injection of indomethacin was followed by a significant increase in the number of sticking and rolling leukocytes. At the submucosal localization, rollers increased from 5.9 - 1.4/0.01 mm 2 /30 s to 34.8 - 13.4/0.01 mm 2 /30 s ( p < .05), and at the mesentery from 8.0 - 2.1/0.01 mm 2 /30 s to 43.1 - 13.5/0.01 mm 2 /30 s ( p < .05). The number of adherent leukocytes measured at the submucosal level went from 0.21 - 0.2/0.01 mm 2 /30 s up to 10.9 - 2.9/0.01 mm 2 /30 s ( p < .05) and at the mesentery from 0.16 - 0.2/0.01 mm 2 /30 s to 15.4 - 3.4/0.01 mm 2 /30 s ( p < .05). The macroscopic ranking showed an ulcer index of 4.93 - 0.76 in the indomethacin group versus 0 in the control group. We found that, despite severe inflammation, this site provided easy and reliable access for IVM. Therefore, we suggest this submucosal site for future studies of intestinal microcirculation in rat models of gut inflammation.

Nanoparticle detachment: a possible link between macro- and nanotribology?

Although particle detachment is a common phenomenon associated with most tribological processes, it seldom occurs that each piece of elemental debris can be considered as the result of a single event. Such an association has been revealed by the systematic study of a specific system, where a pin of graphite is made to rub against thoroughly polished steel. While the discontinuous nature of the transfer film allows a quantitative assessment of the volume of transfer he to be made by 3D optical-profilometry, the linear dependence of the rate of particle detachment dhe/dn (n=number of rubbing cycles) with the logarithm of sliding speed v strongly suggests the existence of a particular type of stick–slip, where each stick may lead to the detachment of a debris particle. The variations in size of these debris with environment as revealed by AFM, further suggest that the global rate of particle detachment is of the form: dhe/dn=Nxei, where N is the number of stick–slip events per rubbing cycle, x the proportion of stick events leading to a cohesive rupture, and ei the mean volume of an elemental particle. While this relation is apparently supported by most experimental results, its actual validation can only be made by experiments at the level of single (nanoscale) asperities, carried out under well-controlled experimental conditions.

Leukocyte Adhesion after Oxidant Challenge in the Hamster Cheek Pouch Microcirculation

Oral administration of S-5682 (Daflon 500 mg, 90% diosmin, 10% hesperidin) inhibits oxidant-induced increase in macromolecular permeability in the postcapillary venules of the hamster cheek pouch microcirculation. In this study, the effect of S-5682 on leukocyte-endothelium interaction was evaluated using the same experimental model. Hamsters kept on a standard diet were divided into 5 groups (n = 6) and treated orally, twice a day, with placebo (10% lactose solution), S-5682, 5, 20 or 80 mg/kg/day (suspended in 10% lactose solution) or α-tocopherol, 1 mg/kg/day, for 10 days prior to the oxidant challenge with tert-butylhydroperoxide (TBOOH). Topical application of TBOOH (10^–4 M for 5 min) to hamsters given acridine orange prior to TBOOH resulted in increases in the number of rolling and sticking (no movement for at least 30 s) leukocytes in postcapillary venules. No changes in the number of rolling leukocytes could be observed in the treated groups compared with the placebo group (p > 0.05). On the contrary, leukocyte adhesion was inhibited in groups treated with S-5682 (5, 20 and 80 mg/kg/day) or α-tocopherol: placebo 105 ± 3/6 mm² (mean ± SEM); S-5682, 5 mg/kg/day 68 ± 3/6 mm² (p < 0.01), 20 mg/kg/day 55 ± 3/6 mm² (p < 0.001) and 80 mg/ kg/day 39 ± 2/6 mm² (p < 0.001) and α-tocopherol 36 ± 1/6 mm² (p < 0.001). The inhibition of oxidant-induced leukocyte adhesion by S-5682 was similar to that seen for ischemia-reperfusion and the higher dose of S-5682 was as effective as α-tocopherol in inhibiting it.

Stick–slip friction in dissimilar polymer pairs used in automobile interiors

The static and dynamic friction of dissimilar pairs of plastics used in automotive interiors was measured as a function of normal load, system stiffness, and surface roughness. Glass fiber filled polypropylene (FPP) was slid on polycarbonate (PC) and glass fiber filled styrene–maleic–anhydride copolymer (SMAC) in a single pass, unidirectional sliding test. The friction was characterized by the value of static coefficient of friction (COF) and the number of stick–slip cycles during sliding. It was found that the FPP/PC and FPP/SMAC pairs had fewer instances of stick slip than FPP/FPP, PC/PC, and SMAC/SMAC pairs except for one of the SMAC polymers. The surface texture which had the smallest average radius of peak curvature, had the lowest value of static COF. The decrease in the static COF of polypropylene (PP) caused by the addition of glass fiber was most likely caused by the increase in elastic modulus and hardness.

Stick knots

In this paper, we will examine the limitations of the superbridge index in providing lower bounds for the stick number of knots, introduce a new invariant which may improve lower bounds on stick number, and discuss how Conway's continued fraction notation for knots may be used to obtain new upper bounds for the stick number of certain infinite classes of knots.

Stick Numbers and Composition of Knots and Links

We address the concept of stick number for knots and links under various restrictions concerning the length of the sticks, the angles between sticks, and placements of the vertices. In particular, we focus on the effect of composition on the various stick numbers. Ultimately, we determine the traditional stick number for an infinite class of knots, which are the (n,n-1)-torus knots together with all of the possible compositions of such knots. The exact stick number was previously known for only seven knots.

Leukocyte-depleting effect of hypothermia on muscle flap microcirculation following ischemia-reperfusion injury

The aim of this study was to determine the effect of leukocyte-endothelial interaction and capillary perfusion on the microcirculation of muscle flaps submitted to ischemia in normothermic and hypothermic conditions. The cremaster muscle flap model was employed. Sixty rats were studied in six groups: normothermic and hypothermic control groups and groups that underwent reperfusion after 4 and 6 hours of ischemia in both normothermic and hypothermic conditions. In each group the following measurements were made: main vessel diameters, red blood cell velocities, the number of perfused capillaries, and the number of leukocytes rolling and sticking in the postcapillary venules. Hypothermia decreased the flow rate significantly and eliminated leukocytes from the microcirculation. Six hours of ischemia under normothermic conditions proved to be lethal for these muscle flaps, whereas hypothermia preserved flap viability.

EFFECTS OF CAROLINA RINSE AND ADENOSINE RINSE ON MICROVASCULAR PERFUSION AND INTRAHEPATIC LEUKOCYTE-ENDOTHELIUM INTERACTION AFTER LIVER TRANSPLANTATION IN THE RAT

Flushing hepatic grafts immediately before revascularization with a specially designed rinse solution such as "Carolina rinse" has been reported to improve survival after liver transplantation in the rat. This study investigated the influence of Carolina rinse and adenosine rinse on early graft function, microcirculation, and leukocyte (WBC)-endothelial cell interaction of arterialized syngeneic orthotopic liver transplants in Lewis rats. Livers were preserved for 24 hr in University of Wisconsin solution and flushed immediately before reperfusion with either Ringer's lactate (group A: n = 7), Ringer's lactate + 0.2 mmol/liter adenosine (group B: n = 6), or Carolina rinse (group C: n = 7). Microvascular perfusion and WBC accumulation were assessed by intravital fluorescence microscopy. In group C, acinar perfusion was significantly improved, accompanied by a lower percentage of nonperfused sinusoids 1 hr after reperfusion (mean +/- SEM: 26 +/- 2% [group A], 21 +/- 2% [B], 11 +/- 1% [C], P < 0.01 for C vs. A or B). In addition, Carolina rinse and, to a lesser extent, adenosine rinse reduced the number of WBC sticking in sinusoids and postsinusoidal venules. Better graft function in group C was indicated by increased bile flow during the observation period of 90 min after reperfusion (0.5 +/- 0.3 ml/100 g liver [group A], 1.5 +/- 0.7 [B], 3.7 +/- 0.6 [C], P < 0.01 for C vs. A or B). We conclude that Carolina rinse is able to improve early excretory hepatocellular function, microvascular perfusion, and intrahepatic WBC accumulation after prolonged cold ischemia and reperfusion, but adenosine is unlikely to be the key component of this rinse solution.

In vivo assessment of acute microvascular injury after reperfusion of ischemic tibialis anterior muscle of the hamster

The purposes of this study were to develope an in vivo model of skeletal muscle ischemia-reperfusion to assess the patterns of microvascular injury, to evaluate a scoring system that permits quantitation of this injury, and to determine in vivo the extent of white blood cell adhesion within the microcirculation during the acute postreperfusion period. Syrian golden hamsters underwent 3.0 or 4.5 hr of lower extremity ischemia without anticoagulation. The microcirculation of the tibialis anterior muscle was visualized by fluorescent intravital microscopy (700X). During the first 1.5 hr of reperfusion the microvascular injury was scored by a grading system based upon the extent of extravasation of fluorosceinlabeled albumin and the degree and level of microvessel obstruction. To correlate the observed changes in the microcirculation to changes in the whole muscle, in a separate group of animals, pH changes in the tibialis anterior muscle were measured at the same time intervals under identical experimental conditions as the microvascular measurements. White blood cells were transiently fluoresced at 1.5 hr after reperfusion by intravenous acridine red and the number of white blood cells rolling (rollers) or sticking (stickers) to the endothelium during a 30-sec observation period was recorded. Two distinct patterns of microvascular injury were seen: after 3.0 hr of ischemia there was a progressive extravasation, some capillary but no arteriolar or venular obstruction, flow velocities increased over time; after 4.5 hr of ischemia there was a greater heterogeneity of injury, primary “no reflow”, extensive capillary, arteriolar, and venular obstruction, as well as a progressive decline in flow velocities. Thrombosis of microvessels was rare. There was no inflow vessel thrombosis. The scoring system showed significant differences, mean (SE), in both the extent of early (30 min) and late (90 min) injuries for the 3.0-hr (early 1.4 (0.6) vs late 2.0 (0.5)) and the 4.5-hr periods of ischemia (early 2.3 (0.9) vs late 3.0 (0.8)). In addition, pH measurements of the tibialis anterior paralleled the changes observed in the microcirculation. There was a significant increase in the number of rolling WBCs, 14.3 (10.3), in the animals undergoing 3.0 hr of ischemia, and in both the number of rollers, 7.4 (4.3), and stickers, 4.0 (1.9), in the animals undergoing 4.5 hr of ischemia compared to those of controls, 1.7 (2.4) and 1.9 (1.5). These results are the first in vivo observations of the pattern of microvascular injury and the extent of white blood cell adhesion in a true muscle of locomotion. We believe that this model will allow further clarification of the mechanisms responsible for the microvascular injury that occurs after reperfusion of ischemic skeletal muscle.

Comparative study on the susceptibility of adult Sitophilus granarius (L.) (Coleoptera: Curculionidae) and larval Galleria mellonella (L.) (Lepidoptera: Pyralidae) to the entomogenous fungus Beauveria bassiana (Bals.) Vuill.

Using standard laboratory methods, the susceptibility of 3rd instar larvae of Galleria mellonella and adults of Sitophilus granarius to the entomogenous fungus Beauveria bassiana was determined. Conidia of the fungus are the active component of the preparation “Boverosil” registered in Czechoslovakia for the control of residual infestations of pests of stored products in grain stores and silos. Virulence against larvae of G. mellonella was measured as an LC 50 value of 1.14 × 10 8 conidia/ml. At this concentration mortality of S. granarius adults was about 3%. An exact LC 50 value could not be determined accurately for adults of S. granarius, but the LC 50 appeared to range between 2 × 10 8 and 5 × 10 8 conidia/ml. The extent of mortality of S. granarius appeared to be affected by the number of conidia sticking to the insect's body at the start of the test, i.e. during the 2 hr exposure of the insect to the sprayed suspension before mixing with excess grain. During this period the r.h. was 100%, dropping below 90% after mixing, by which time the impact of spore concentration was reduced to a minimum.